This research study is a Phase II clinical trial. Phase II clinical trials test the effectiveness of an investigational drug to learn whether the drug works in treating a specific cancer. "Investigational" means that the drug is still being studied and that research doctors are trying to find out more about it-such as the safest dose to use, the side effects it may cause, and if the drug is effective for treating different types of cancer. It also means that the FDA has not approved this drug for use patients undergoing adjuvant treatment for HER2+ breast cancer. Trastuzumab emtansine (T-DM1) is a drug that may stop cancer cells from growing. This drug has been used in other research studies and information from those other research studies suggests that this drug may help to prevent the recurrence of breast cancer in this research study.